Arent they all science vessels? Janeway sure did act like science took priority over getting home. Even the dedicated warship Defiant made science survey missions
Do we ever hear Starfleet refer to Federation ships as cruiser, destroyer frigate, etc?
In "A Taste of Armageddon" Anan 7 twice calls the
Enterprise a star cruiser.
ANAN: All security personnel, Federation prisoners have escaped. They are to be found. They are armed. If they resist, do what is necessary. Planetary disruptor banks, calculate orbit of star cruiser now circling. Stand by to fire. Full power.
ANAN: In ten seconds, open fire. Destroy the star cruiser. Those are the orders of the Council.
In "The Way to Eden" a presumably civilian ship is called a cruiser:
SPOCK: It is definitely the stolen space cruiser, Captain, the Aurora. I read six aboard.
CAPTAINS LOG: Captain's log, stardate 5832.3. The son of the Catullan ambassador is one of six we have beamed aboard from the stolen cruiser Aurora. We have been ordered to handle him with extreme delicacy, because the treaty negotiations now in progress between the Federation and Catualla are in a crucial phase.
KIRK: Lieutenant Palmer, notify Starbase we have the six aboard who stole the space cruiser Aurora. Regrettably, the space cruiser itself was destroyed.
KIRK: But we don't steal space cruisers and act like irresponsible children. KIRK
Star Trek III: The Search For Spock:
TORG: Yes. ...Federation Battle Cruiser. Have they scanned us?
Of course it is a Klingon who describes the
Enterprise as a battle cruiser.
In "Relics":
SCOTT: I actually served on two. This was the first. She was also the first ship I ever served on as Chief Engineer. You know, I served aboard eleven ships. Freighters, cruisers, starships, but this is the only one I think of. The only one I miss.
Scott counts cruisers and starships as different types of Starfleet vessels.
The Arsenal of Freedom":
ANNOTATION: Captain's log, stardate 41798.2. We have been ordered by Starfleet to proceed to the Lorenze Cluster and investigate the disappearance of a light cruiser, USS Drake, which was in that system trying to unravel a mystery of its own which began when recent long range probes indicated that all intelligent life on the planet Minos has disappeared.
According to Memory Alpha, the 3rd edition of the Star Trek Encyclopedia describes the Drake as:
According to the
Star Trek Encyclopedia (3rd ed., p. 122) this vessel was a
Wambundu-class starship, with the
registryNCC-20381.
http://memory-alpha.wikia.com/wiki/USS_Drake_(2364)
But the various editions of the Star Trek Encyclopedia seem to have differing informatin about the Drake.
In "Conspiracy":
WORF: Captain, sensors are detecting three Federation starships already in orbit around the planet.
PICARD: Identify.
WORF: Two are frigates. The Renegade commanded by Tryla Scott, and the Thomas Paine, Captain Rixx commanding.
DATA: The third is just coming into range now, sir. It is Ambassador Class heavy cruiser, USS Horatio.
It is not odd that Worf considers an Ambassador Class heavy cruiser a starship, but it is more unusual that Worf considers two frigates to be starships.
"Sacrifice of Angels":
SISKO: Sisko to all ships. Cruiser and Galaxy wings, drop to half impulse. You too, Commander.
And:
NOG: Attack fighters in Theta formation. Cruiser and Galaxy wings at half impulse.
Sisko says Galaxy class starships are not cruisers, so perhaps they are counted as battleships during the war. He didn't say what classes of ships are counted as cruisers.
SISKO: Mister O'Brien, have Destroyer units two and six move in closer. They need more cover fire. And tell Captains Diego and Reynolds to stay alert. They may try to outflank us.
So there are ships described as destroyers in the Federation fleet.
In "Judgement" Captain Archer identifies himself as:
ARCHER: Captain Archer of the battle cruiser Enterprise.
Of course NX class spaceships of the United Earth Starfleet are not the same as Federation Starships centuries later.
So the various classifications of Starfleet fighting vessels are not very clear. Which is not too surprising since the uniforms that Captain Ramart and navigator Tom Nellis of the
Antares wear in "Charlie X" look like Starfleet uniforms:
Captain's Log, star date 1533.6. Now manoeuvring to come alongside cargo vessel Antares. Its Captain and First officer are beaming over to us with an unusual passenger.
KIRK: This must be a space first. A transport ship that doesn't need anything?
Captain's Log, star date 1535.8. UESPA headquarters notified of the mysterious loss of science probe vessel Antares.
SPOCK: Your mind is not on the game, Captain. Check. The Antares?
KIRK: A survey ship with twenty men aboard lost. No reason. Obviously, Captain Ramart was not aware of any trouble. I can't figure it.
http://www.chakoteya.net/StarTrek/8.htm
So Kirk describes the
Antares as having four different types of assignments, missions or duties!
http://memory-alpha.wikia.com/wiki/Antares